Air Conditioner Size Calculator (BTU per Square Foot)

Enter the room size and the type of building. For top floor, ceiling height, sun and so on, choose the options that apply and they are applied as correction factors (if you are not sure, leave them as they are).

Units

What to calculate

Room size

AC cooling capacity (kW)

AC heating capacity (kW, optional)

Cooling load per tatami (W, optional)

Heating load per tatami (W, optional)

Top floor or right under the roof

Ceiling height

Sun and windows (cooling)

Open to the kitchen

Climate (heating)

Extra correction factor (optional)

Metric mode follows the sizing method of Japanese air conditioner catalogs: the room size is converted to tatami mats (1 tatami = 1.62 m²), and the standard load depends on the building (cooling: wood frame 350, concrete 230 W per tatami; heating: wood frame 440, concrete 350 W per tatami) when the load fields are blank. All correction factors are estimates.

Result and graph

Enter the room size on the left and press "Calculate". The capacity you need, the matching air conditioner size and a graph will appear here.

[ CLOSE ]

What you can do on this page
What is this calculation used for?
How to Use
Formula
Symbols and terms
- Symbols
- Terms
Good to know before you start
How to calculate it in Excel
How to calculate it in Google Sheets
How to calculate it in Python
How to write it in LaTeX and other math languages (copy and paste)
How to have ChatGPT do the calculation
DataChef Features
Related Features
NumberChef Calculators List

What you can do on this page

Enter the floor area in square feet, and you instantly get the cooling and heating capacity you need in BTU/h, plus the matching common air conditioner size (5,000, 8,000, 12,000 BTU/h and so on)
Choose the conditions of the room, such as top floor, ceiling height, strong sun, open kitchen or cold climate, and the capacity is adjusted with a correction factor (the factors are estimates and you can change them)
You can also work backward: enter the cooling or heating capacity of an air conditioner and find how many square feet it can handle
A graph plots the capacity needed against the floor area, with lines for the common sizes (5,000, 6,000, 8,000 BTU/h …), so you can see at a glance where your room falls
How to read the sizing chart, a plain-language explanation of the formulas, and copy-and-paste formulas for Excel, Google Sheets and Python are all on this page

The results are only a guide. Sizing charts assume a typical room with average insulation, so the capacity you really need depends on insulation, window size, layout and climate. Before you buy, describe your room to the store or the installer and ask for advice (for central systems, a professional load calculation). This page only answers "what size of air conditioner do I need". For running costs, use the electricity cost calculator.

What is this calculation used for?

Choosing the AC size for each room when you move or build

When you buy air conditioners for a new home, find the capacity each room needs from its area and match it to a size. For example, a 12 ft × 12 ft bedroom (144 ft²) needs \(144 \times 20 = 2{,}880\) BTU/h, so a 5,000 BTU/h unit is enough. A 20 ft × 18 ft living room open to the kitchen (360 ft², kitchen factor 1.1) needs \(360 \times 20 \times 1.1 = 7{,}920\) BTU/h, so an 8,000 BTU/h unit is the guide.
Each step up in size also costs more, so knowing "which room needs which size" in numbers first makes it easier to compare prices and quotes.

Checking whether a room stays hot because the AC is too small

If a room never cools down to the thermostat setting on a hot day, a common reason is that the air conditioner is too small for the room. If a 400 ft² living room has a 5,000 BTU/h window unit, the room needs \(400 \times 20 = 8{,}000\) BTU/h, so the unit has only \(5{,}000 \div 8{,}000 = 62.5\%\) of the capacity needed.
An undersized unit runs at full power all the time, which also raises the electric bill. When you replace it, choosing a size at least as large as the capacity needed usually improves both comfort and cost. (A unit that is much too large is not good either: it cools the room quickly but turns off before it removes enough humidity.)

Deciding whether an AC can be moved to another room

When you move or switch rooms, you may want to reuse a window unit you already have. Enter its 8,000 BTU/h in the "Room size from capacity" mode and you get \(8{,}000 \div 20 = 400\) ft². A 15 ft × 20 ft room (300 ft²) has room to spare, while a 22 ft × 20 ft room (440 ft²) is a little too large.
Also check that the window fits the unit and that the outlet matches its plug (most small units use a standard 115 V outlet, while large ones may need a 230 V outlet).

Checking whether the AC in a rental fits the room

In a rental, the air conditioner that comes with the unit is sometimes small for the room. Look at the label on the unit (or look up its model number) to find its cooling capacity in BTU/h, and enter it in the "Room size from capacity" mode. A 6,000 BTU/h unit covers about \(6{,}000 \div 20 = 300\) ft².
If you find that "a 350 ft² room has a unit rated for about 300 ft²", you have a concrete reason to talk to the landlord or property manager before you move in.

Estimating whether a home-size AC is enough for a small office

For a small office or shop room, such as a 500 ft² meeting room, the rule of thumb gives \(500 \times 20 = 10{,}000\) BTU/h. A room where many people gather or with many computers and lights gives off more heat, so add an extra correction factor of about 1.2: \(10{,}000 \times 1.2 = 12{,}000\) BTU/h, a 12,000 BTU/h (1 ton) unit. This keeps the estimate from coming up short.
If you need more than 36,000 BTU/h (3 tons), or the space has a very high ceiling, it is a job for a commercial HVAC system, so talk to an HVAC contractor.

Formula

Floor area of the room (ft²)

Standard notation (the usual math form)

\(A\) \(=\) \(L\) \(\times\) \(W\)

In words (symbols replaced with words)

③ \(A\): floor area (ft²) \(=\) ① \(L\): length (ft) \(\times\) ② \(W\): width (ft)

The formula in words

① Take the \(L\): length (ft)

② multiply it by the \(W\): width (ft)

③ and you get the \(A\): floor area (ft²)

Quick example

The floor area of a bedroom that is 12 ft long and 12.5 ft wide is

\(A\): floor area (ft²) \(=\) length (12 ft) \(\times\) width (12.5 ft)

\(12 \times 12.5 = 150\)

Key idea

Measure the room wall to wall and multiply. For an L-shaped room, split it into rectangles and add the areas. For an open plan space, such as a living room with a kitchen, add up all the area you want to cool. If your measurements include inches, turn them into feet first (12 ft 6 in = 12.5 ft). If you know the area in square meters, multiply by about 10.76 (1 m² ≈ 10.764 ft²). The area found here is the starting point for the next formulas.

Cooling capacity needed (BTU/h)

Standard notation (the usual math form)

\(Q_{c}\) \(=\) \(A\) \(\times\) \(q_{c}\) \(\times\) \(k_{c}\)

In words (symbols replaced with words)

④ \(Q_c\): cooling capacity needed (BTU/h) \(=\) ① \(A\): floor area (ft²) \(\times\) ② \(q_c\): cooling load per ft² (BTU/h) \(\times\) ③ \(k_c\): cooling correction factor

The formula in words

① Take the \(A\): floor area (ft²)

② multiply it by the \(q_c\): cooling load per ft² (BTU/h) to get the cooling power the whole room needs

③ multiply by the \(k_c\): cooling correction factor to add room for the conditions of the room

④ and you get the \(Q_c\): cooling capacity needed (BTU/h)

Quick example

The cooling capacity needed for a 150 ft² bedroom (20 BTU/h per ft², no correction) is

\(Q_c\): cooling capacity needed (BTU/h) \(=\) floor area (150 ft²) \(\times\) cooling load (20 BTU/h per ft²) \(\times\) correction factor (1)

\(150 \times 20 \times 1 = 3{,}000\)

Key idea

You need at least 3,000 BTU/h, so the matching size is the smallest common size at or above it: 5,000 BTU/h, the smallest window unit you usually find in stores. Always pick "the smallest size that is at least what you need". The cooling load per ft² is how much cooling power (BTU/h) one square foot of room needs. This calculator uses 20 BTU/h per ft², the rule of thumb widely used in the US. It is a straight-line summary of the ENERGY STAR sizing chart for room air conditioners, which lists, for example, 5,000 BTU/h for 100 to 150 ft², 8,000 BTU/h for 300 to 350 ft², 12,000 BTU/h for 450 to 550 ft² and 18,000 BTU/h for 700 to 1,000 ft². Small rooms need a little more per ft² and large rooms a little less, so check your result against that chart too. The same chart suggests adjustments: 10% more for a very sunny room, 10% less for a heavily shaded room, 600 BTU/h more for each person beyond two, and 4,000 BTU/h more if the unit is used in a kitchen.

Heating capacity needed (BTU/h)

Standard notation (the usual math form)

\(Q_{h}\) \(=\) \(A\) \(\times\) \(q_{h}\) \(\times\) \(k_{h}\)

In words (symbols replaced with words)

④ \(Q_h\): heating capacity needed (BTU/h) \(=\) ① \(A\): floor area (ft²) \(\times\) ② \(q_h\): heating load per ft² (BTU/h) \(\times\) ③ \(k_h\): heating correction factor

The formula in words

① Take the \(A\): floor area (ft²)

② multiply it by the \(q_h\): heating load per ft² (BTU/h) to get the heating power the whole room needs

③ multiply by the \(k_h\): heating correction factor to add room for the conditions of the room

④ and you get the \(Q_h\): heating capacity needed (BTU/h)

Quick example

The heating capacity needed for the same 150 ft² bedroom (25 BTU/h per ft², no correction) is

\(Q_h\): heating capacity needed (BTU/h) \(=\) floor area (150 ft²) \(\times\) heating load (25 BTU/h per ft²) \(\times\) correction factor (1)

\(150 \times 25 \times 1 = 3{,}750\)

Key idea

The formula has exactly the same shape as for cooling. Only the load per ft² and the correction factor change to the heating values. This calculator uses 25 BTU/h per ft² for heating, about 1.25 times the cooling value. In winter, the gap between the outdoor temperature and the room temperature is larger than in summer (for example, 32°F outside and 68°F inside is a 36°F gap, while 95°F outside and 78°F inside is only 17°F), so the same room needs more power to heat than to cool. In this example, cooling needs 3,000 BTU/h but heating needs 3,750 BTU/h. If you will heat with a heat pump (a mini-split, for example), check that its heating capacity is at least this value. In cold climates, the heat you need can be much larger, and the heating capacity of an ordinary heat pump drops as the outdoor air gets colder, so also look at cold-climate heat pumps.

How to find the correction factor

Standard notation (the usual math form)

\(k\) \(=\) \(k_{1}\) \(\times\) \(k_{2}\) \(\times\) \(k_{3}\) \(\times\) \(k_{4}\)

In words (symbols replaced with words)

⑤ \(k\): correction factor \(=\) ① \(k_1\): top floor \(\times\) ② \(k_2\): ceiling height \(\times\) ③ \(k_3\): sun or climate \(\times\) ④ \(k_4\): open kitchen

The formula in words

① Take the \(k_1\): top floor (1.1 if it applies, otherwise 1)

② multiply by the \(k_2\): ceiling height (standard 1, high 1.1, vaulted 1.2)

③ multiply by the \(k_3\): sun or climate (cooling: 1.1 if very sunny; heating: 1.2 in a cold climate)

④ multiply by the \(k_4\): open kitchen (1.1 if the room is open to the kitchen)

⑤ and you get the \(k\): correction factor (an item that does not apply is multiplied as 1, which changes nothing)

Quick example

The cooling correction factor for a room on the top floor (1.1) with a high ceiling (1.1), normal sun (1) and an open kitchen (1.1) is

\(k_c\): cooling correction factor \(=\) top floor (1.1) \(\times\) high ceiling (1.1) \(\times\) normal sun (1) \(\times\) open kitchen (1.1)

\(1.1 \times 1.1 \times 1 \times 1.1 = 1.331\)

Key idea

The correction factor tells you how much extra capacity to allow compared with a typical room. A factor of 1 means no extra, 1.1 means 10% more, and 1.331 means about 33% more capacity is needed. When two or three conditions apply, the factors are multiplied, so the extra adds up. The cooling factor \(k_c\) and the heating factor \(k_h\) use slightly different items. Strong sun matters only for summer cooling, so it goes into the cooling factor only. A cold climate matters only for winter heating, so it goes into the heating factor only. Top floor, ceiling height and an open kitchen affect both seasons, so they go into both. If you enter an extra correction factor, it goes into both too. The values 1.1 and 1.2 are estimates used by this calculator. If you know your situation, such as a very well insulated home (less extra) or an old home with many windows (more extra), adjust with the extra correction factor.

Room size an AC can handle (working backward)

Standard notation (the usual math form)

\(A\) \(=\) \(T\) \(\times\) \(12000\) \(\div\) \((\) \(q\) \(\times\) \(k\) \()\)

In words (symbols replaced with words)

⑤ \(A\): floor area it can handle (ft²) \(=\) ① \(T\): AC capacity (tons) \(\times\) ② 12,000 (tons → BTU/h) \(\div\) \((\) ③ \(q\): load per ft² (BTU/h) \(\times\) ④ \(k\): correction factor \()\)

The formula in words

① Take the \(T\): AC capacity (tons)

② multiply it by 12,000 to turn it into BTU/h

③ divide by the \(q\): load per ft² (BTU/h)

④ multiplied by the \(k\): correction factor (this product is the load per ft² including the correction)

⑤ and you get the \(A\): floor area it can handle (ft²)

Quick example

The room size a 1-ton (12,000 BTU/h) air conditioner can cool (20 BTU/h per ft², no correction) is

\(A\): floor area it can handle (ft²) \(=\) cooling capacity (1 ton) \(\times\) 12,000 \(\div\) \((\) cooling load (20 BTU/h per ft²) \(\times\) correction factor (1) \()\)

\(1 \times 12{,}000 \div (20 \times 1) = 600\)

Key idea

This is the "cooling capacity needed" formula solved for the floor area \(A\) (the formula turned around). If the capacity is already in BTU/h, as on most window units, skip the × 12,000 step: \(A = Q \div (q \times k)\). A 1-ton (12,000 BTU/h) unit can cool about 600 ft² with no correction. On the top floor with strong sun (factor 1.1 × 1.1 = 1.21), it is \(12{,}000 \div (20 \times 1.21) = 495.8\ldots\), or about 495 ft². In this mode the calculator rounds the area down to a whole square foot, because rounding up could suggest a room that is slightly too large for the unit. The ENERGY STAR sizing chart lists 12,000 BTU/h for 450 to 550 ft², a little smaller than the 20 BTU/h rule gives, so treat the result as the upper end. If you also enter a heating capacity, the same formula with the heating load (25 BTU/h per ft²) and the heating factor gives the area it can heat.

The air conditioner capacity you need is "floor area (ft²) × load per ft² (BTU/h) × correction factor", and you choose the smallest common size at or above that value (5,000, 6,000, 8,000, 10,000, 12,000 BTU/h …). A common rule of thumb is 20 BTU/h per ft² for cooling, and heating needs somewhat more. To find the room size a unit can handle, solve the same formula for the floor area.

Symbols and terms

Symbols

\(A\)	A	The floor area of the room (ft²), from the first letter of "area".
\(L\), \(W\)	L, W	The length and width of the room (ft). Multiplied together, they give the floor area \(A\).
\(q_c\), \(q_h\)	q sub c, q sub h	The cooling load and heating load per ft² (BTU/h). The letter \(q\) is often used for an amount of heat, and the small \(c\) and \(h\) stand for cooling and heating. The standard values in this calculator are 20 for cooling and 25 for heating.
\(k_c\), \(k_h\)	k sub c, k sub h	The correction factors for cooling and heating. The letter \(k\) is often used for a coefficient (a constant). They are found by multiplying the factors for each condition, \(k_1\) to \(k_4\). If no condition applies, they are 1.
\(Q_c\), \(Q_h\)	capital Q sub c, capital Q sub h	The cooling and heating capacity needed (BTU/h). They are the load per ft² \(q\) spread over the whole room (multiplied by the area), so a capital \(Q\) is used to tell them apart from the small \(q\).
\(T\)	T	The capacity of an air conditioner in tons, used when working backward (1 ton = 12,000 BTU/h). If the capacity is given in BTU/h, divide it directly by the load per ft². Use the cooling capacity to find the area it can cool, or the heating capacity to find the area it can heat.
BTU/h	BTU per hour	The unit of air conditioner capacity in the US - how much heat the unit can move out of (or into) the room in one hour. 1 BTU (British thermal unit) is the heat that warms 1 pound of water by 1°F. 1 kW = 3,412 BTU/h, and 12,000 BTU/h is called 1 ton of cooling. Labels often write just "BTU".

Terms

rated cooling capacity	The cooling power an air conditioner delivers under set test conditions, shown on the box and label as "Cooling Capacity 12,000 BTU/h". This is the number that sets the size of the unit.
rated heating capacity	The heating power a heat pump delivers under set test conditions (usually 47°F outdoors). It is often a little larger than the cooling capacity of the same model, but it drops as the outdoor air gets colder.
sizing chart	A table that matches room sizes to air conditioner capacities. The best known in the US is the ENERGY STAR chart for room air conditioners (for example, 100 to 150 ft² → 5,000 BTU/h, 250 to 300 ft² → 7,000 BTU/h, 450 to 550 ft² → 12,000 BTU/h). It assumes a typical room, so adjust for sun, shade, people and kitchens.
ton	A unit of cooling capacity used for central air and larger units. 1 ton = 12,000 BTU/h, the cooling from melting one ton of ice in 24 hours. A 2-ton system is 24,000 BTU/h.
Manual J	The standard method used by HVAC professionals in the US to calculate the heating and cooling load of a home room by room, from insulation, windows, climate and more. For central air or a whole-house heat pump, ask for a Manual J calculation instead of relying on square feet alone.
standard sizes	The capacities that home air conditioners are usually sold in. For window and portable units and mini-splits, common sizes are 5,000, 6,000, 8,000, 10,000, 12,000, 15,000, 18,000, 24,000, 30,000 and 36,000 BTU/h. This calculator picks the smallest of these that is at least the capacity you need.
heat load	The amount of heat that has to be removed from (or added to) a room per hour to keep its temperature. It is the total of heat moving through walls and windows, sunlight, and heat from people and appliances. The summer part is the cooling load and the winter part is the heating load. The "load per ft²" on this page is this amount shared out per square foot.
cooling load	The amount of heat that has to be removed from a room per hour in summer to keep its temperature (the cooling version of the heat load). It includes heat coming in through walls and windows, sunlight, and heat from people and appliances.
heating load	The amount of heat that has to be added to a room per hour in winter to keep its temperature (the heating version of the heat load). It makes up for the heat escaping through walls and windows.
correction factor	A multiplier that shows how much extra capacity to allow compared with a typical room. It is made by multiplying the factors for conditions such as top floor, ceiling height, strong sun, open kitchen and cold climate. If no condition applies, it is 1.
cold-climate heat pump	A heat pump designed to keep most of its heating capacity even when the outdoor air is very cold. An ordinary heat pump loses heating capacity as the temperature drops, so in cold regions people choose models with extra heating capacity or cold-climate models.
tatami	The Japanese room size unit, the size of one tatami mat. When you switch "Units" to Metric, this page uses the method of Japanese air conditioner catalogs: the area is converted to tatami at 1 tatami = 1.62 m² (the Japanese real estate standard), and the load depends on whether the building is wood frame or reinforced concrete.

Good to know before you start

Here is what helps you use the calculation on this page with real understanding, not just by pressing the button.
If you get stuck, going back to these topics is the quickest way forward.

Multiplying and dividing decimals (Grades 5–6)	Being able to multiply with decimals, as in \(150 \times 20 \times 1.1\) Being able to divide by a product, as in \(12{,}000 \div (20 \times 1.21)\) Being able to turn feet and inches into decimal feet (6 in = 0.5 ft, so 12 ft 6 in = 12.5 ft)
Percents and multipliers (Grades 6–7)	Knowing that "×1.1" means 10% more and "×1.2" means 20% more Knowing that two multipliers in a row are multiplied together (\(1.1 \times 1.2 = 1.32\))
Area and unit conversion (Grades 3–6)	Knowing that the area of a rectangle is length × width, measured in square feet (ft²) Knowing that k (kilo) means 1,000, so \(1\,\mathrm{kW} = 1{,}000\,\mathrm{W}\), and that 1 kW is about 3,412 BTU/h
Energy and heat (middle school science)	Knowing that BTU/h and watts both measure energy per unit of time, and can be used for electricity and for heat Knowing that heat flows from warmer to colder places, and flows faster when the temperature difference is larger (the reason heating needs more capacity than cooling)

How to calculate it in Excel

Copy the whole table below and paste it into cell A1 in Excel. It works as is.

Table to find the floor area

Length (ft)	12
Width (ft)	12.5
Floor area (ft²)	=B1*B2

Table to find the cooling capacity needed (BTU/h)

Floor area (ft²)	150
Cooling load per ft² (BTU/h)	20
Cooling correction factor	1
Cooling capacity needed (BTU/h)	=B1B2B3

Table to find the heating capacity needed (BTU/h)

Floor area (ft²)	150
Heating load per ft² (BTU/h)	25
Heating correction factor	1
Heating capacity needed (BTU/h)	=B1B2B3

Table to find the correction factor

Top floor factor	1.1
Ceiling height factor	1.1
Sun (cooling) or climate (heating) factor	1
Open kitchen factor	1.1
Correction factor	=B1B2B3*B4

Table to find the room size an AC can handle (working backward)

AC capacity (BTU/h)	12000
Load per ft² (BTU/h)	20
Correction factor	1
Floor area it can handle (ft²)	=B1/(B2*B3)

After pasting, the upper cells in column B are your inputs and the formula cells are calculated automatically.
The first table finds the floor area of a 12 ft × 12.5 ft room: B3 shows 150 (ft²). The second table is the cooling example for that room: B4 shows 3000 (BTU/h), so the smallest common size at or above it is 5,000 BTU/h. The third table is heating for the same room: B4 shows 3750 (BTU/h).
The fourth table multiplies the correction factors: B5 shows 1.331. Put this value in B3 of the second or third table to include the correction. The fifth table works backward: for a 12,000 BTU/h unit at 20 BTU/h per ft², B4 shows 600 (ft²).

How to calculate it in Google Sheets

Copy the whole table below and paste it into cell A1 in Google Sheets. It works as is.

Table to find the floor area

Length (ft)	12
Width (ft)	12.5
Floor area (ft²)	=B1*B2

Table to find the cooling capacity needed (BTU/h)

Floor area (ft²)	150
Cooling load per ft² (BTU/h)	20
Cooling correction factor	1
Cooling capacity needed (BTU/h)	=B1B2B3

Table to find the heating capacity needed (BTU/h)

Floor area (ft²)	150
Heating load per ft² (BTU/h)	25
Heating correction factor	1
Heating capacity needed (BTU/h)	=B1B2B3

Table to find the correction factor

Top floor factor	1.1
Ceiling height factor	1.1
Sun (cooling) or climate (heating) factor	1
Open kitchen factor	1.1
Correction factor	=B1B2B3*B4

Table to find the room size an AC can handle (working backward)

AC capacity (BTU/h)	12000
Load per ft² (BTU/h)	20
Correction factor	1
Floor area it can handle (ft²)	=B1/(B2*B3)

These formulas use only multiplication and division, so the same formulas as in Excel work as is. Copy the whole table, paste it into cell A1, and replace the numbers in column B with the values for your room.

How to calculate it in Python

area_ft2 = 150             # floor area (ft²), e.g. a 12 ft x 12.5 ft room
cooling_factor = 1.0       # cooling correction factor (e.g. top floor 1.1 x high ceiling 1.1 x ...)
heating_factor = 1.0       # heating correction factor

# Load per ft² (BTU/h). Standard values of this calculator
cooling_load = 20
heating_load = 25

# Capacity needed (BTU/h) = area x load x correction factor
cooling_btu = area_ft2 * cooling_load * cooling_factor
heating_btu = area_ft2 * heating_load * heating_factor

# Common sizes (BTU/h). Pick the smallest one that is at least the cooling capacity needed
sizes = [5000, 6000, 8000, 10000, 12000, 15000, 18000, 24000, 30000, 36000]
chosen = next((s for s in sizes if s >= cooling_btu), None)

print(f"Cooling needed: {cooling_btu:,.0f} BTU/h ({cooling_btu / 3412:.2f} kW) / Heating needed: {heating_btu:,.0f} BTU/h")
if chosen:
    print(f"Matching size: {chosen:,} BTU/h")
else:
    print("More than 36,000 BTU/h (consider two or more units or central air)")

Runs with the standard library only. Change the first three values (floor area and the cooling and heating correction factors) to match your room and run it. For the 150 ft² example, it prints cooling 3,000 BTU/h (0.88 kW), heating 3,750 BTU/h, and a matching size of 5,000 BTU/h.

How to write it in LaTeX and other math languages (copy and paste)

Floor area of the room (ft²)

A = L × W

A = L \times W

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>A</mi>
    <mo>=</mo>
    <mi>L</mi>
    <mo>&#xD7;</mo>
    <mi>W</mi>
  </mrow>
</math>

A = L * W

area = length*width

A := L*W;

A = L*W;

A = L×W

Cooling capacity needed (BTU/h)

Qc = A × qc × kc

Q_c = A \times q_c \times k_c

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <msub><mi>Q</mi><mi>c</mi></msub>
    <mo>=</mo>
    <mi>A</mi><mo>&#xD7;</mo><msub><mi>q</mi><mi>c</mi></msub><mo>&#xD7;</mo><msub><mi>k</mi><mi>c</mi></msub>
  </mrow>
</math>

Q_c = A * q_c * k_c

coolingBtu = area*coolingLoad*coolingFactor

Q_c := A*q_c*k_c;

Q_c = A*q_c*k_c;

Q_c = A×q_c×k_c

Heating capacity needed (BTU/h)

Qh = A × qh × kh

Q_h = A \times q_h \times k_h

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <msub><mi>Q</mi><mi>h</mi></msub>
    <mo>=</mo>
    <mi>A</mi><mo>&#xD7;</mo><msub><mi>q</mi><mi>h</mi></msub><mo>&#xD7;</mo><msub><mi>k</mi><mi>h</mi></msub>
  </mrow>
</math>

Q_h = A * q_h * k_h

heatingBtu = area*heatingLoad*heatingFactor

Q_h := A*q_h*k_h;

Q_h = A*q_h*k_h;

Q_h = A×q_h×k_h

How to find the correction factor

k = k₁ × k₂ × k₃ × k₄

k = k_1 \times k_2 \times k_3 \times k_4

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>k</mi>
    <mo>=</mo>
    <msub><mi>k</mi><mn>1</mn></msub>
    <mo>&#xD7;</mo>
    <msub><mi>k</mi><mn>2</mn></msub>
    <mo>&#xD7;</mo>
    <msub><mi>k</mi><mn>3</mn></msub>
    <mo>&#xD7;</mo>
    <msub><mi>k</mi><mn>4</mn></msub>
  </mrow>
</math>

k = k_1 * k_2 * k_3 * k_4

factor = k1*k2*k3*k4

k := k1*k2*k3*k4;

k = k1*k2*k3*k4;

k = k_1×k_2×k_3×k_4

Room size an AC can handle (working backward)

A = T × 12000 ÷ (q × k)

A = \frac{T \times 12000}{q \times k}

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>A</mi>
    <mo>=</mo>
    <mfrac>
      <mrow><mi>T</mi><mo>&#xD7;</mo><mn>12000</mn></mrow>
      <mrow><mi>q</mi><mo>&#xD7;</mo><mi>k</mi></mrow>
    </mfrac>
  </mrow>
</math>

A = (T * 12000) / (q * k)

area = tons*12000/(load*factor)

A := T*12000/(q*k);

A = T*12000/(q*k);

A = (T×12000)/(q×k)

How to have ChatGPT do the calculation

You are a calculation assistant for choosing an air conditioner. Do the following calculation by actually running Python code, and base your answer only on the numbers from the execution result (do not answer by mental math or guessing).

A room is 20 ft long and 18 ft wide. Find its floor area in square feet.
The cooling load is 20 BTU/h per ft² and the heating load is 25 BTU/h per ft². The room is on the top floor (factor 1.1), the ceiling is standard (factor 1), the sun is normal (factor 1), it is open to the kitchen (factor 1.1), and the climate is average (factor 1).
Find the cooling capacity needed (BTU/h) as "floor area × cooling load × cooling correction factor" and the heating capacity needed (BTU/h) as "floor area × heating load × heating correction factor". The cooling factor is top floor × ceiling × sun × kitchen, and the heating factor is top floor × ceiling × kitchen × climate.
Find each of the following:
1. The floor area (ft²)
2. The cooling and heating correction factors
3. The cooling and heating capacity needed (BTU/h, rounded to a whole number)
4. Among the common sizes 5,000, 6,000, 8,000, 10,000, 12,000, 15,000, 18,000, 24,000, 30,000 and 36,000 BTU/h, the smallest one that is at least the cooling capacity needed

Show the formulas you used and the numbers from the execution result.

How to Use

1

Enter your numbers

Type the numbers you want to calculate with into the input fields
2

Calculate

Press the "Calculate" button
3

Check the result

The result appears on the spot. The same page also explains the idea behind the calculation and the formula